Question: Simplify the following expression: $\dfrac{12p^3}{42p}$ You can assume $p \neq 0$.
Solution: $ \dfrac{12p^3}{42p} = \dfrac{12}{42} \cdot \dfrac{p^3}{p} $ To simplify $\frac{12}{42}$ , find the greatest common factor (GCD) of $12$ and $42$ $12 = 2 \cdot 2 \cdot 3$ $42 = 2 \cdot 3 \cdot 7$ $ \mbox{GCD}(12, 42) = 2 \cdot 3 = 6 $ $ \dfrac{12}{42} \cdot \dfrac{p^3}{p} = \dfrac{6 \cdot 2}{6 \cdot 7} \cdot \dfrac{p^3}{p} $ $\phantom{ \dfrac{12}{42} \cdot \dfrac{3}{1}} = \dfrac{2}{7} \cdot \dfrac{p^3}{p} $ $ \dfrac{p^3}{p} = \dfrac{p \cdot p \cdot p}{p} = p^2 $ $ \dfrac{2}{7} \cdot p^2 = \dfrac{2p^2}{7} $